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On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation

Abstract

Ion channels are large transmembrane proteins that are able to conduct small inorganic ions. They are characterized by high selectivity and the ability to gate, i.e. to modify their conductance in response to different stimuli. One of the types of gating follows the ball and chain model, according to which a part of the channel’s protein forms a ball connected with the intracellular side of the channel by a polypeptide chain. The ball is able to modify the conductance of the channel by properly binding to and plugging the channel pore. In this study, the polypeptide ball is treated as a Brownian particle, the movements of which are limited by the length of the chain. The probability density of the ball’s position is resolved by different diffusional operators — parabolic (including the case with drift), hyperbolic, and fractional. We show how those different approaches shed light on different aspects of the movement. We also comment on some features of the survival probabilities (which are ready to be compared with electrophysiological measurements) for issues based on the above operators.

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Correspondence to Krzysztof Małysiak.

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Paper authored by participants of the international conference: International Workshop on Ionic Channels, Szczyrk, Poland, May 27 – June 01, 2007. Publication cost was covered by the organisers of this meeting.

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Małysiak, K., Grzywna, Z.J. On the possible methods for the mathematical description of the ball and chain model of ion channel inactivation. Cell Mol Biol Lett 13, 535–552 (2008). https://doi.org/10.2478/s11658-008-0015-8

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  • DOI: https://doi.org/10.2478/s11658-008-0015-8

Key words

  • Voltage-gated ion channel
  • N-inactivation
  • Hyperbolic diffusion
  • Subdiffusion